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Solve each equation for $x$ .

$$(a)2^{x-5}=3 \quad \text { (b) } \ln x+\ln (x-1)=1$$

(a) $x=5+\log _{2} 3$(b) $x=\frac{1+\sqrt{1+4 e}}{2} \approx 2.223$

Calculus 1 / AB

Chapter 1

Functions and Sequences

Section 5

Logarithms; Semilog and Log-Log Plots

Functions

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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this question asks us to solve each equation for Axe. Let's take the log of both sides of the base too, so we can cancel off the two on the left hand side. Leaving us with acts is five close long to the base, two of three for part B. We're following a similar route. We know this is essentially natural. Log of X minus one. Writing this and factored form naturally, Axe times X minus one is a corpulent to natural log of E which gives us ax squared minus acts minus. He is equivalent to zero. We know that if we're using the core jack formula, we can write this as one plus squirt of one plus for E divided by two, or you can leave it as the fraction.

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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